Electromagnetic Theory: A refresher (or introduction...)

James Clerk Maxwell (wiki) and work by others essentially proved that light is an electromagnetic wave. The development of classical electrodynamics leads to a picture of light as a continuous wave that transports energy. However, quantum mechanics provides a different explanation where light is quantized into elementary particles called photons. The quantum mechanical picture of light as a photon is not particularly useful in optics. There are definitely times where it makes sense, but in most cases, especially in this course, we will use the model of light as a wave.

The distinction between particle and wave nature of light is most often taken to be that light propagates like a wave and acts like a particle during the emission and absorption process. Light is created and destroyed in quanta or photons an not continuously like a classical wave however, its propagation through everyday obstructions is governed by its wave characteristics.

A pretty good (and often infuriating) analogy is the flow of traffic (LINK)

waves in traffic

Each vehicle in the video represents a single "quanta", but en masse -- behave more like fluid flowing with density fluctuations potentially caused by geographic features like blind corners or hills.

Observing the right most lanes of traffic, you will notice a density fluctuation in the vehicles that actually travels in the OPPOSITE direction of the flow of traffic. This phenomenon has an optical counterpart that we will revisit later in the semester.

Overall, the average behavior of traffic is relatively constant from day to day, so the precise motion of each vehicle is irrelevant. To finish the analogy, the energy transported by a large number of photons is, *on average*, the same as the energy transferred by a classical electromagnetic wave. These are a few of the reasons we rely on the classical picture rather than the tedious, and often, less useful quantum mechanical picture of light. So we proceed with the model of light as a classical electromagnetic wave with the understanding that in some cases, this model does not describe reality. In this course, we will do our best to avoid those scenarios.

Later in the semester, we will discuss a series of approximations that move away from light as a wave and toward a more useful formalism where light is treated simply as a mathematical ray. This is known as the Geometric optics approach and is valid when the wavelength is very small compared to the characteristic length scale in a system, such as the diameter of a lens or similar. Physical Optics is a slightly more complicated model for the propagation of light through an optical system that we will investigate as well. In the physical optics approach, the wave nature of light plays a more prominent role than in the geometric optics limit.